We assume the basics of Hopf algebra and coalgebra theory, as covered in, say, [1]}, [2]}. Comultiplications, counits, and antipodes are denoted as usual by \(\Delta ,\varepsilon \)  and \(S\)  perhaps adorned with the name of the coalgebra or Hopf algebra as in \(\Delta _H\) , and we use Sweedler notation with suppressed summation symbol for comultiplication, as in \(\displaystyle \Delta (x)=x_1\otimes x_2\) . Comodules are always right and finite-dimensional, and everything in sight is complex.
